Dactyloscopy is fingerprinting, a way of identifying and distinguishing between individuals by their individual fingerprints. It has become the tool of choice for police and other investigative agencies.
Bertillonage, also called anthropometry, is a way of identifying individuals by measuring distinct parts of their bodies and the relationships between them. Bertillonage is named for a Paris policeman, Alphonsxe Bertillon, who noted that adults don't grow or change much after the age of 20, and so each adult has distinct measurements, such as the size of their head, arms, legs, and so on.
The Bertillon method spread throughout the world and was very accurate, though it proved to be not as accurate as fingerprinting. It was phased out when two men imprisoned at Fort Leavenworth, Kansas, who claimed to be unrelated, had the same identical appearance and measurements. (It turned out that they were estranged twin brothers, which explains the similarities in their Bertillon measurements.) At any rate, they had different fingerprints, which sealed the case for dactyloscopy over Bertillonage.
That's just as well, because anthropometric methods have been misused so often; in the 1890s in England, for instance, it was used to measure head size to "prove" that Irish and Africans were "lesser species"; and later it was used by the Nazis to "prove" that Jews were inferior to the "Aryan race."
Here's more about the Bertillon method from the New York State Division of Criminal Justice Services. That state and many others in the U.S. used the Bertillon system before fingerprinting became widely used.
New York's Bureau of Identification, started in 1896, took the
Bertillon measurements of every criminal who entered the system. This
enabled them to find that many "first offenders" were actually repeat
offenders. These efforts led shortly thereafter to the founding of the
National Bureau of Investigation, the forerunner to the FBI.
The New York State website also has fascinating information about the beginning of the use of fingerprinting (dactyloscopy, remember?) by police throughout the world. Madame L hopes you'll follow the link to learn more about it, if you're interested.